"It is a rumor," district spokeswoman Shana Kemp said in response.
As in the past, Ackerman, who spoke after a dramatic special meeting of the School Reform Commission, emphasized that she did not seek her current job but was asked to come to Philadelphia, and that her work is not done.
"As far as I know, the SRC, the mayor, and all those people who are critical to my staying are still on board, and very much focused on moving forward with Imagine 2014," Ackerman said, referencing her five-year strategic plan.
Asked by reporters multiple times if he continued to support Ackerman, Mayor Nutter did not answer the question directly.
He said that the superintendent's boss is the SRC, not the mayor, and noted that the SRC has yet to complete its annual review of Ackerman. He also pointed to some school success stories.
"We've seen numerous improvements, and to some extent the numbers do speak for themselves," Nutter said.
Ackerman did acknowledge that she signed a letter last week delegating to Deputy Superintendent Leroy Nunery the authority to sign district documents during July and August. But she said it was routine paperwork, recommended by attorneys, and district officials said similar documents had been signed in the past, most recently in May.
Nunery defended the document, noting that SRC resolutions call on Ackerman "or her designee" to execute contracts and sign documents.
"This is how most large organizations are run, a succession plan and a plan for action. People have jumped to conclusions," Nunery said.
And yes, the superintendent said, she is going on vacation this summer.
"I plan to take some time," she said. "I haven't taken a vacation in three years. I guess you could say that it's long overdue, and I won't apologize," Ackerman said.
Kemp would not say exactly how long Ackerman would be gone.
The superintendent, Kemp said in a statement, "will be spending some time with her family and friends for a brief period this summer, while the majority of students are on break, as she continues doing the important work of addressing the educational needs of the young people attending district schools."
The SRC met Monday to authorize the collection of city taxes for the district. After the measure passed unanimously, some parents questioned district decisions.
Rebecca Poyourow, parent of a child at Cook-Wissahickon Elementary in Roxborough, asked the SRC to shift money back into classrooms. The district is facing a budget gap that was as large as $629 million, and has laid off more than 3,400 employees and made cuts to programs to compensate.
The SRC has set July 1 as a deadline for the district's five unions to negotiate $75 million in givebacks. If they do not, it has said it will vote to cancel the contracts and impose terms on them.
"Are you a body that will pay for the mismanagement of the school system by breaking teachers' contracts . . . or can you find the collective will to cut nonessential contracts and programs, as well as central administration positions? What is the legacy you wish to leave?" Poyourow asked.
Helen Gym, a founder of Parents United for Public Education, blasted the district for not sharing with the public a document leaked to Public School Notebook listing schools that might be closed in the next few years.
The document was not among those sent to the city by the district, despite a recently signed Educational Accountability Agreement giving the city more oversight.
Gym said that parents - many of whom lobbied legislators over the last few months for more funding - are "not the enemy, and we deserve to be treated better than this."
She called for hearings on school closings and on the district's leadership, which she said is no longer effective.
Officials said the school closing document was an internal working document. There were 18 meetings around the city soliciting input, Nunery said, and more will be held.
To shed 70,000 empty seats, officials seek to close up to 50 schools in the next few years.
Imagining that the document was final is "jumping so far to conclusions that it's laughable," Nunery said.
Though Ackerman and the closing document faced stiff criticism from some, Emmanuel Bussie of GOTV America, a community-involvement advocacy group, said the district needs Ackerman.
"Please, Dr. Ackerman, don't go," Bussie said.
"Not going," Ackerman responded from her seat at the front of the room.
Bussie, who believes the SRC should be dissolved and replaced with an elected school board, also took issue with those who criticized the district.
"There should be fewer attacks," Bussie said, "and more ideas."
Also at the SRC meeting, Human Resources chief Estelle Matthews said the district was in the process of recalling 174 laid-off teachers who will be saved with part of the $53 million in new money given to the district by the city.
The 174 kindergarten-through-third-grade teachers will be informed this week about their reinstatement.
Contact staff writer Kristen Graham at 215-854-5146, email@example.com or @newskag on Twitter. Read her blog, "Philly School Files," at www.philly.com/schoolfiles.
Inquirer staff writers Marcia Gelbart, Troy Graham, and William K. Marimow contributed to this article.